Question

PQ is the perpendicular bisector of MN. What is MP?

Answer 1

The length of MP is 28 units.

In a triangle with PQ as the perpendicular bisector of MN, the Perpendicular Bisector Theorem states that the segment MP is equal in length to NP. Therefore, in triangle PNM:

MP = NP

Given that NP = 6x + 1 and MP = 10x - 17, we can set these equal to each other:

6x + 1 = 10x - 17

Now, solve for x:

17 = 10x - 6x - 1

17 = 4x - 1

18 = 4x

`\[ x = (18)/(4) \]`

x = 4.5

Now that we have the value of x, we can find the length of MP:

MP = 10x - 17

MP = 10(4.5) - 17

MP = 45 - 17

MP = 28

So, the length of MP is 28 units.